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Record Nr. |
UNINA9910788898703321 |
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Autore |
Tu Loring W. |
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Titolo |
Hodge theory and the local Torelli problem / / Loring W. Tu |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , [1983] |
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©1983 |
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ISBN |
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Descrizione fisica |
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1 online resource (72 p.) |
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Collana |
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Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 279 |
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Disciplina |
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Soggetti |
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Curves, Algebraic |
Surfaces, Algebraic |
Hodge theory |
Torelli theorem |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Nota di bibliografia |
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Bibliography: pages 55-56. |
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Nota di contenuto |
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""Table of Contents""; ""Introduction""; ""I. Variation of Hodge structure""; ""Â1. The period map""; ""Â2. The Hodge bundles in the smooth case""; ""Â3. The Hodge bundles when there are singular fibers""; ""The log complex""; ""Relative dualizing sheaf""; ""The canonical extension""; ""Â4. A multiplicative formula for the holomorphic Euler characteristic""; ""Â5. Monodromy""; ""Â6. Mixed Hodge structures and the numerical invariants of a degeneration""; ""6.1. Varieties with normal crossings""; ""6.2. The limiting mixed Hodge structure""; ""6.3. The Clemensâ€?Schmid exact sequence"" |
""6.4. Genus of a singular curve""""II. Local Torelli for curves""; ""Â7. The case of no singular fibers""; ""Â8. With singular fibers""; ""8.1. First proof: mixed Hodge structure and the topology of the singular fiber""; ""8.2. Second proof: using the relative dualizing sheaf to map X into a projective space""; ""8.3. Third proof: the ample cone on the moduli space M""; ""III. Local Torelli in higher dimensions""; ""Â9. Surfaces with large irregularity""; ""Â10. Threefolds and fourfolds with large irregularity""; ""Bibliography""; ""List of Notations""; ""Index""; ""A""; ""B""; ""C"" |
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